Question: Solve for $x$ and $y$ using elimination. ${x-3y = -11}$ ${-x-4y = -38}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-7y = -49$ $\dfrac{-7y}{{-7}} = \dfrac{-49}{{-7}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x-3y = -11}\thinspace$ to find $x$ ${x - 3}{(7)}{= -11}$ $x-21 = -11$ $x-21{+21} = -11{+21}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {-x-4y = -38}\thinspace$ and get the same answer for $x$ : ${-x - 4}{(7)}{= -38}$ ${x = 10}$